Some Induced Correlated Aggregating Operators with Interval Grey Uncertain Linguistic Information and Their Application to Multiple Attribute Group Decision Making

Abstract

We propose the interval grey uncertain linguistic correlated ordered arithmetic averaging (IGULCOA) operator and the induced interval grey uncertain linguistic correlated ordered arithmetic averaging (I-IGULCOA) operator based on the correlation properties of the Choquet integral and the interval grey uncertain linguistic variables to investigate the multiple attribute group decision making (MAGDM) problems, in which both the attribute weights and the expert weights are correlative. Firstly, the relative concepts of interval grey uncertain linguistic variables are defined and the operation rules between the two interval grey uncertain linguistic variables are established. Then, two new aggregation operators: the interval grey uncertain linguistic correlated ordered arithmetic averaging (IGULCOA) operator and the induced interval grey uncertain linguistic correlated ordered arithmetic averaging (I-IGULCOA) operator are developed and some desirable properties of the I-IGULCOA operator are studied, such as commutativity, idempotency, monotonicity, and boundness. Furthermore, the IGULCOA and I-IGULCOA operators based approach is developed to solve the MAGDM problems, in which both the attribute weights and the expert weights are correlative and the attribute values take the form of the interval grey uncertain linguistic variables. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.